Separation of Variables

Separation of Variables for the Wave Equation

In this video, I illustrate the process of separation of variables by solving the wave equation on a finite interval with Neumann boundary conditions. Tune in for an adventure through PDEs, ODEs, and Fourier series! Enjoy

[edmundwoolliams]

Excellent, full explanation of a separation of variables solution! I think this is missing in many textbooks and lecture courses I’ve seen

[sirelegant]

Amazing explanation Dr., grateful for your work

[l_szabi]

"Peyam saves the day!"

*drops eraser into eternal void

[nicoghspy]

Great video as always. At the end I thought you would split the sum in two sums, one dependent of Am and the other dependent of Bm, so you could say that second sum is only that one term. I think it would make it look very elegant

[ranam]

Very good explanation that I missed in college

[ziedjbeli]

thank you, you' re very helpful, keep up.

[m.a.]

By the way, you can just use the Kronecker delta function instead of the weird "0"
So the term becomes: [δ_(3, M)* B_M * sin(MCt)].

[rodrigolopez]

I think that this is the only way that i know to solve a second order PDE, does it work with every 2nd order PDE? what about PDE's of greaters orders? or more general, how can we know "a priori" if a PDE eq can be solved with separation of variables? If it fails, which other methods exist?


Thank you very much cause your effort and this amazing content, I really appreciate it

[azhar]

I usually use m^2 instead of lambda for convenience

[batu]

hey dr peyam i think sep of vars is the hardest method. 1hour for 1 problem. is separation of variables powerful technique? that can solve different kinds of pdes?

[bs]

please could you solve this integral

dx/(sqrt(sinx) + cosx)^4

[ruffifuffler]

The longer story of bleeding, entanglement, pruning, and grafting.

[m.a.]

Shouldn't it be T double dot instead of T double prime, as you are differentiating with respect to time?